Solve the equation using the Quadratic Formula.x squared minus 8 x plus 12 equals 0Question content area bottomPart 1Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.A.x​ =enter your response here​(Simplify your answer. Use integers or fractions for any numbers in the expression. Type an exact​ answer, using radicals as needed. Use a comma to separate answers as​ needed.)B.There are no real solutions.

Answer 1

To solve the equation \(x^2 - 8x + 12 = 0\) using the Quadratic Formula, we first identify the coefficients:

• \(a = 1\)
• \(b = -8\)
• \(c = 12\)

The Quadratic Formula is given by:

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

Now, let's calculate the discriminant \(b^2 - 4ac\):

\[ b^2 - 4ac = (-8)^2 - 4(1)(12) = 64 - 48 = 16 \]

Since the discriminant is positive (\(16 > 0\)), there will be two real solutions.

Now we apply the Quadratic Formula:

\[ x = \frac{-(-8) \pm \sqrt{16}}{2 \cdot 1} = \frac{8 \pm 4}{2} \]

Now we can find the two solutions:

1. First solution: \[ x = \frac{8 + 4}{2} = \frac{12}{2} = 6 \]

2. Second solution: \[ x = \frac{8 - 4}{2} = \frac{4}{2} = 2 \]

Thus, the solutions to the equation \(x^2 - 8x + 12 = 0\) are:

A. \(x = 6, 2\)

So, the final answer would be:

Answer: \(x = 6, 2\)